DarkGamer, 1 year ago

Quantum computers aren't faster because they "process" multiple "possibilities" at once.

@hetscop I thought eigenstates/qbits were what made quantum computing faster and gave it its additional capabilities. For example, if you had an 8-bit integer represented by a bunch of qbits in a superposition of states, it would have every possible value from 0-256 and could be computed with as though it were every possible value at once until it is observed, the probability wave collapses, and a finite value emerges. Is this not the case?

I read up a bit on Shor's algorithm, and while I don't fully understand it all it seems to take advantage of superposition of states destructively, which sounds a lot like "processing multiple possibilities at once."

When we input a superposition through our system and measure the remainder, we get a superposition of all possible powers that result in only that remainder. And this remaining superposition repeats with a period of the power [math didn't paste nicely]

Just as a classical Fourier Transform translates a wave as a function of time into a function of frequency, so too does a Quantum Fourier Transform (QFT), with a superposition as an output with a frequency of the input.

So, if we input a single state into a QFT, the output will be a superposition of states with varying weights or probabilities that form a wave with the input state as the frequency. And if we input multiple states into a QFT, the output will be a superposition of superpositions - with destructive and constructive interference combining superpositions into one wave. And if our input to the QFT is a superposition with period [math didn't paste nicely] source

If my understanding is inaccurate, can you recommend a good source to understand this? Thanks!